In this talk, we will give a introduction on the scaling limit of partition function of a random walk in a heavy-tailed spatially correlated random environment of moving-average form in  $(1+1)$-dimensional. The spatial covariance of the environment has long-range decay with Hurst parameter $H=\frac32-r\in(1/2,1)$. We identify the limiting fluctuations of the log-partition function in the intermediate disorder regime and show that the critical tail exponent is $\alpha_c=\frac{3}{H}=\frac{6}{3-2r}$.When $\alpha>\alpha_c$, the model has the same scaling limits as the corresponding Gaussian spatially correlated polymer. In the heavy-tail regime $2<\alpha\le\alpha_c$, under the scale $\beta_N=\beta/l(N^{3/2})$, the log-partition function still satisfies Gaussian fluctuation at scale $\beta_NN^{H/2}$.The main technical tools, as well as an invariance principle for polynomial chaos, are measure transformation and multiscale arguments to ensure that the truncation method can be used to derive the limits.